Do you know of any sealant I should use on the concrete before I carpet over the top of it?

Depending on the size of the leaks I'd throw on some O'Henry's roof sealant on there until you find a more reasonable rate.   

But I'll won't use siliconized acrylic caulk to get them in, I won't leave the sash weights in the cavities or half-heartedly jam some.fiberglass into them, I'm not going to trust cheap sealant and adhered untreated wood trim to keep the basement windows  in place when someone starts trying to kick them in.

We will also apply a sealant once the countertops are insalled .Don't be lured into the countertops you might see online starting at $19.99 per square foot.

Nowadays we'd use an epoxy sealant and/or plastic sheeting...

I emailed him about it after I searched the work and the time between coats and he said he used a dry torch for the sealant or whatever it's called and said he performed work that should have cost me $14k.

Applying a sealant product to any framing members (joists and studs) after the chemical treatment will probably also be a good idea to follow.

This is easy to do with off the shelf sealant and an applicator.

It needs minor cosmetics and possibly a basement sealant.

One leak is often a popped nail, or a shingle either loosened or blown off in a windy storm or perhaps a leak around a chimney where the sealant has cracked a bit...or the cracked boot.